INSTABILITY OF THE SCALING THEORY OF 2-D LOCALIZATION

A conventional description of electron quantum diffusion by means of one-parameter renormalization group (RG) has been shown to be unstable. The evidence has resulted from the instability of the zero-component nonlinear matrix sigma -model with respect to inclusion of certain symmetry-breaking terms. It gives rise to an infinite number of relevant RG charges increasing infinitely fast at the very initial state of RG transformations and affecting conductance in a nonperturbative way. Thus the one-parameter RG approach by Abrahams et al. fails to have a microscopic basis.